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C₂×#12839 #493819

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

952 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 66 points:

(1,2);(3,4)(5,15)(6,21,23,11)(7,25)(8,28)(9,13)(10,18)(12,16)(14,26)(17,42,44,35)(19,48)(20,37)(22,52,54,55)(24,33,53,51)(27,56)(29,43,49,65)(30,47)(31,58)(32,40,50,62)(34,41)(36,39)(38,46)(45,60,64,63)(57,66,59,61);(3,5,16,39,8,19,27,47,9,20,41,58,26,46,7,18)(4,10,25,38,14,31,34,37,13,30,56,48,28,36,12,15)(6,17,40,61,24,45,54,65,23,44,62,66,53,64,22,43)(11,29,55,60,33,57,50,42,21,49,52,63,51,59,32,35);(3,6)(4,11)(5,17)(7,22)(8,24)(9,23)(10,29)(12,32)(13,21)(14,33)(15,35)(16,40)(18,43)(19,45)(20,44)(25,55)(26,53)(27,54)(28,51)(30,49)(31,57)(34,50)(36,59)(37,42)(38,60)(39,61)(41,62)(46,64)(47,65)(48,63)(52,56)(58,66)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401015);